The proof of this proposition relies on the blossom shrinking operation:
starting from the graph \(G\)  with a matching \(M\) , this consists in taking the
quotient graph \(G^{\prime }\)  where all the vertices of the blossom have been identified;
\(M\)  induces a matching \(M^{\prime }\)  in \(G^{\prime }\) . This operation is also central in
combinatorial matching algorithms, starting with Edmonds's blossom
algorithm [1]}.
